Question: Multiply. $64.09 \times52 = ~$
Solution: $6{,}409 \times52$ and $64.09\times52$ multiply the same digits in the same order. So, the product of both problems will also have the same digits in the same order. Let's multiply $6{,}409\times 52$. Then we can estimate to place the decimal point in the product of $64.09 \times 52$. $\begin{aligned} 6{,}409&\\ \underline{ \times 52}&\\ 18}\\ 0}\\ 800}\\ 12{,}000}\\ 450}\\ 0}\\ 20{,}000}\\ \underline{+300{,}000}}\\ 333{,}268 \end{aligned}$ Let's estimate to place the decimal in $64.09 \times52$. $\begin{aligned} 64.09 \times 52 &\approx 60\times 50\\\\ &\approx3{,}000 \end{aligned}$ Where can we place the decimal in $333{,}268$ to get a product close to $3{,}000$ ? $64.09 \times52 = 3{,}332.68$